**AMS Chelsea Publishing**

Volume: 359;
1976;
303 pp;
Hardcover

MSC: Primary 20;
**Print ISBN: 978-0-8218-4229-4
Product Code: CHEL/359.H**

List Price: $50.00

Individual Member Price: $45.00

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#### Supplemental Materials

# Character Theory of Finite Groups

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*I. Martin Isaacs*

Character theory is a powerful tool for
understanding finite groups. In particular, the theory has been a key
ingredient in the classification of finite simple groups. Characters
are also of interest in their own right, and their properties are
closely related to properties of the structure of the underlying
group.

The book begins by developing the module theory of complex group
algebras. After the module-theoretic foundations are laid in the
first chapter, the focus is primarily on characters. This enhances the
accessibility of the material for students, which was a major
consideration in the writing. Also with students in mind, a large
number of problems are included, many of them quite challenging.

In addition to the development of the basic theory (using a cleaner
notation than previously), a number of more specialized topics are
covered with accessible presentations. These include projective
representations, the basics of the Schur index, irreducible character
degrees and group structure, complex linear groups, exceptional
characters, and a fairly extensive introduction to blocks and Brauer
characters.

This is a corrected reprint of the original 1976 version, later
reprinted by Dover. Since 1976 it has become the standard reference
for character theory, appearing in the bibliography of almost every
research paper in the subject. It is largely self-contained, requiring
of the reader only the most basic facts of linear algebra, group
theory, Galois theory and ring and module theory.

#### Table of Contents

# Table of Contents

## Character Theory of Finite Groups

#### Readership

Graduate students and research mathematicians interested in finite groups, character theory, and representation theory.